📐

Complex Numbers

★★★☆☆High School

📖Definition

A number combining real and imaginary parts, written as a + bi where i² = -1.

📐Formulas

z = a + bi

Standard form of complex number

  • aReal part
  • bImaginary part
  • iImaginary unit (i² = -1)
|z| = √a² + b²

Absolute value (modulus)

\barz = a - bi

Complex conjugate

(a+bi)(c+di) = (ac-bd) + (ad+bc)i

Complex multiplication

✏️Examples

예제 1☆☆☆☆

Calculate (3 + 2i) + (1 - 4i).

예제 2★★☆☆☆

Calculate (2 + 3i)(1 - 2i).

Applications

Electrical Engineering

AC circuit analysis

Physics

Quantum mechanics, waves

Computer Graphics

2D rotation, fractals

#number#complex#imaginary#advanced